Spontaneous Parametric Down-Conversion Experiment to Measure Both Photon Trajectories and Double-Slit Interference

Recent work using spontaneous parametric down-conversion (SPDC) has made possible investigations of the Einstein-Podolsky-Rosen paradox in its original (position-momentum) form. We propose an experiment that uses SPDC photon pairs to measure through which slit a photon passes while simultaneously observing double-slit interference.Comment: 6 pages, 1 figur

Contributions to Pion Decay from Lorentz Violation in the Weak Sector

Lorentz violation in the weak sector would affect the beta-decay lifetimes of pions. The decay amplitude may be rendered anisotropic, but only an isotropic violation of boost invariance can affect the net lifetime in the center of mass frame. However, since the rest frames of the pions that produce the NuMI neutrino beam at Fermilab vary with the rotation of the Earth, it is possible to constrain anisotropic Lorentz violation using prior analyses of sidereal variations in the event rate at the MINOS near detector. The resulting bounds on weak-sector Lorentz violation are at the 10^(-4) level, a substantial improvement over previous results. The highly relativistic character of the pions involved is responsible for the improvement.Comment: 16 page

Absence of Long-Wavelength Cerenkov Radiation With Isotropic Lorentz and CPT Violation

Modified theories of electrodynamics that include violations of Lorentz symmetry often allow for the possibility of vacuum Cerenkov radiation. This phenomenon has previously been studied in a number of Lorentz-violating theories, but none of the methods that have previously been developed are sufficient to study a theory with a timelike Chern-Simons term $k_{AF}$, because such a term may generate exponentially growing solutions to the field equations. Searching for vacuum Cerenkov radiation in a theory with a purely timelike Chern-Simons term using only elementary methods, we find that, despite the presence of the runaway modes, a charge in uniform nonrelativistic motion does not radiate energy, up to second order in the velocity.Comment: 9 page

Non-Hermitian Interactions Between Harmonic Oscillators, with Applications to Stable, Lorentz-Violating QED

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra $su(2)$. The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard $a^{\dag}$ and $a$. The new operators also give rise to a natural family of two-oscillator couplings. These nonlinear couplings are not generally self-adjoint, but their low-energy limits are self-adjoint, exactly solvable, and stable. We discuss the structure of a theory involving these couplings. Such a theory might have as its ultra-low-energy limit a Lorentz-violating Abelian gauge theory, and we discuss the extremely strong astrophysical constraints on such a model.Comment: 11 page

Lorentz Violation in Fermion-Antifermion Decays of Spinless Particles

If Lorentz and CPT violation exist, they could affect the decays of scalar and pseudoscalar particles. For a decay into a fermion and an antifermion (not necessarily of the same mass), both the total decay rate and the outgoing particle distribution may be modified, through interference between the conventional decay mechanism and a separate Lorentz-violating mechanism. The modifications are sensitive to forms of Lorentz violation that are otherwise rather difficult to study, since at tree level they do not affect particle propagation, but only interaction vertices. Using existing experimental data on charged pion decay, it is possible to constrain three parameters in the modified pion-muon-neutrino coupling at better than the $10^{-9}$ level; these are the first bounds on these quantities.Comment: 16 page

Nonunitary Quantum Theory with a Field Cutoff

We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple (1+1)-dimensional version of this theory, we may calculate the results of certain scattering processes exactly. The main feature of the nontrivial solutions is the appearance of shock fronts, whose time development is irreversible. The resulting nonunitarity implies that these theories are, at a minimum, radically different from conventional quantum field theories.Comment: 12 pages, 1 figure; additional references adde

Consequences of Neutrino Lorentz Violation For Leptonic Meson Decays

If the observation by OPERA of apparently superluminal neutrinos is correct, the Lagrangian for second-generation leptons must break Lorentz invariance. We calculate the effects of an energy-independent change in the neutrino speed on another observable, the charged pion decay rate. The rate decreases by an factor [1 - 3/(1 - (m_mu)^2 / (m_pi) ^ 2) ( - 1)], where is the (directionally averaged) neutrino speed in the pion's rest frame. This provides a completely independent experimental observable that is sensitive to the same forms of Lorentz violation as a neutrino time of flight measurement.Comment: 10 page

Radiatively Induced Lorentz-Violating Photon Masses

We examine the radiative corrections to an extension of the standard model containing a Lorentz-violating axial vector parameter. At second order in this parameter, the photon self-energy is known to contain terms that violate gauge invariance. Previously, this has been treated as a pathology, but it is also possible to take the gauge noninvariant terms at face value. These terms then make Lorentz-violating contributions to the photon mass, and directly measured limits on the photon mass can be used to set bounds on the Lorentz violation at better than the 10^-22 GeV level.Comment: 12 pages, minor changes and updated reference

There is No Ambiguity in the Radiatively Induced Gravitational Chern-Simons Term

Quantum corrections to Lorentz- and CPT-violating QED in flat spacetime produce unusual radiative corrections, which can be finite but of undetermined magnitude. The corresponding radiative corrections in a gravitational theory are even stranger, since the term in the fermion action involving a preferred axial vector $b^{\mu}$ would give rise to a gravitational Chern-Simons term that is proportional $b^{\mu}$, yet which actually does not break Lorentz invariance. Initially, the coefficient of this gravitational Chern-Simons term appears to have the same ambiguity as the coefficient for the analogous term in QED. However, this puzzle is resolved by the fact that the gravitational theory has more stringent gauge invariance requirements. Lorentz symmetry in a metric theory of gravity can only be broken spontaneously, and when the vector $b^{\mu}$ arises from spontaneous symmetry breaking, these specific radiative corrections are no longer ambiguous but instead must vanish identically.Comment: 16 page

Lorentz and CPT Violation in Scalar-Mediated Potentials

In Lorentz- and CPT-violating effective field theories involving scalar and spinor fields, there exist forms of Lorentz violation that modify only the scalar-spinor Yukawa interaction vertices. These affect low-energy fermion and antifermion scattering processes through modifications to the nonrelativistic Yukawa potentials. The modified potentials involve novel combinations of momentum, spin, and Lorentz-violating background tensors.Comment: 16 page